Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 4x - 8$ and $ KL = 9x - 23$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {4x - 8} = {9x - 23}$ Solve for $x$ $ -5x = -15$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 4({3}) - 8$ $ KL = 9({3}) - 23$ $ JK = 12 - 8$ $ KL = 27 - 23$ $ JK = 4$ $ KL = 4$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {4} + {4}$ $ JL = 8$